What is the extreme f(x)=2x^6-6x^4 ?

The extreme f(x)=2x^6-6x^4 is Minimum(-sqrt(2),-8),Maximum(0,0),Minimum(sqrt(2),-8)

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extreme f(x)=2x^6-6x^4

extreme points

f (x) = 2 x^{6} - 6 x^{4}

Minimum (- 2, - 8), Maximum (0, 0), Minimum (2, - 8)

Solution steps

f^{'} (x) = 12 x^{5} - 24 x^{3}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

2 x^{6} - 6 x^{4} : - 8

Minimum (- 2, - 8)

Plug

x = 0

into

2 x^{6} - 6 x^{4} : 0

Maximum (0, 0)

Plug

x = 2

into

2 x^{6} - 6 x^{4} : - 8

Minimum (2, - 8)

Minimum (- 2, - 8), Maximum (0, 0), Minimum (2, - 8)

What is the extreme f(x)=2x^6-6x^4 ?
The extreme f(x)=2x^6-6x^4 is Minimum(-sqrt(2),-8),Maximum(0,0),Minimum(sqrt(2),-8)